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A349622
Numbers k for which 2k-1 can be obtained with successive prime shifts towards larger primes (by iterating A003961, starting from k).
1
1, 2, 3, 7, 19, 25, 26, 31, 33, 37, 79, 93, 97, 139, 157, 199, 211, 229, 271, 307, 331, 337, 367, 379, 439, 499, 547, 577, 601, 607, 619, 661, 691, 727, 811, 829, 841, 877, 937, 967, 979, 997, 1009, 1034, 1069, 1171, 1237, 1279, 1297, 1399, 1429, 1459, 1531, 1609, 1627, 1657, 1759, 1867, 2011, 2029, 2089, 2131, 2137
OFFSET
1,2
COMMENTS
Numbers k for which A246277(2k-1) = A246277(k). This in turn implies a looser condition A046523(2k-1) = A046523(k).
Nonsquarefree terms are rare: 25, 841 (= 29^2), 970225 ( = 5^2 * 197^2), ..., also 414690595, which is not a square. Some of these are also terms of A048674. Compare to A348511.
PROG
(PARI)
A246277(n) = if(1==n, 0, my(f = factor(n), k = primepi(f[1, 1])-1); for (i=1, #f~, f[i, 1] = prime(primepi(f[i, 1])-k)); factorback(f)/2);
isA349622(n) = (A246277(n)==A246277(n+n-1));
CROSSREFS
Subsequences: A005382 (primes present), A048674 (terms requiring only one iteration to reach 2k-1).
Cf. also A348511.
Sequence in context: A178954 A138111 A218100 * A078373 A038878 A040112
KEYWORD
nonn
AUTHOR
Antti Karttunen, Nov 26 2021
STATUS
approved